In various wavelength ranges from soft X-rays to hard X-rays in a third-generation light radiation facility represented by the SPring-8, it has become possible to use X-rays having characteristics of high brightness, low emittance, and high coherence. This has significantly improved sensitivity and spatial resolution of various analyses such as a fluorescent X-ray analysis, photoemission spectroscopy, and X-ray diffraction. Such X-ray analyses or X-ray microscopy using the light radiation not only exhibit high sensitivity and high resolution but also enable nondestructive observation, and therefore are currently expected to be used in fields such as medicine, biology, and material science.
In the light radiation facility, a focused X-ray nanobeam is necessary for adding the high spatial resolution to various analysis techniques using an X-ray. In an X-ray nanobeam formation, a focusing optical device employing a method using a reflective mirror is recognized as most advantageous due to high brightness and no chromatic aberration. As a focusing optical system using a reflective mirror, a Kirkpatrick and Baez (K-B) mirror is generally used (see Patent Document 1).
In order to perform a good focusing, it is necessary to prepare a focusing mirror with high accuracy. The focusing mirror is manufactured by processing a block of silicon single crystal into a predetermined shape using a conventional method, and then performing a finish processing with ultraprecision using a numerically controlled elastic emission machining (EEM). The accuracy of the focusing mirror manufactured by this process greatly depends on the accuracy of a surface shape measurement before the processing. The inventors of the present invention have proposed a microstitching interferometry (MSI) in Non-Patent Document 1, and have already established a system of measuring with high accuracy the shape of an X-ray mirror with a measurement reproducibility of less than or equal to 1 nm in PV value in all spatial wavelength ranges. Further, as a system that enables measurement of a curved surface having a large curvature, a relative angle determinable stitching interferometry (RADSI) has been completed. A measurement principle thereof is based on a shape measurement by stitching using a Michelson microscope interferometer in which a high spatial resolution can be expected, and a stitching error is corrected using data of a Fizeau interferometer capable of a highly-accurate measurement in spatial wavelength ranges of intermediate to long periods. In this stitching, the degree of coincidence in a commonly measured overlapping range is used out of shape measurement data of adjacent ranges, and the inclination of adjacent measurement data is optimally corrected.
As described above, the inventors of the present invention have completed a surface processing and measurement system with nanometer precision, manufactured an X-ray focusing mirror having an accuracy of 2 nm (PV value), and have succeeded in a diffraction-limited focusing of hard X-rays at a sub-30 nm level with the SPring-8. However, although the shape measurement with stitching using the interferometer described above enables measurement of the surface shape of the focusing mirror with high accuracy, there is a drawback that collecting data takes a long period of time and data processes thereafter also takes time. Even if the shape of the focusing mirror can be measured with high accuracy using a shape measurement device using the interferometer under specific ideal conditions, the shape of a reflective surface of the focusing mirror is not ensured in a state where the focusing mirror is incorporated in an X-ray condensing device. The reason is because environment conditions such as temperature, external stress, or the like normally differ between when the shape of the focusing mirror is measured and when the X-ray condensing device is actually used. In order to achieve the most ideal focusing with diffraction limitation, it is necessary to know the shape of the reflective surface of the X-ray mirror in the incorporated state in the X-ray condensing device with high accuracy, but there has been no system of measuring the shape of the focusing mirror in the operated state in approximately real time among X-ray focusing optical systems.
One method of an imaging performance measurement of a projection lens or the like is the phase restoration method. The phase restoration method is a method that has been used mainly to improve resolution in optical systems such as an electron microscope or an astronomical telescope in which a large aberration exists. Basically, the phase distribution of an image is obtained from the intensity distribution of the image on a focus plane and a pupil plane, and the wavefront aberration of the optical system is calculated from the phase distribution (see Patent Document 2 or 3). In the normal phase restoration method, an arbitrary phase is first provided to the measured intensity distribution at the focus plane, and then a Fourier transformation is performed to obtain the complex amplitude distribution at the pupil plane. Next, out of the obtained complex amplitude distribution, a phase portion of the obtained CAD is left as it is, while only an absolute value corresponding to an intensity portion is substituted with a value according to an actual measured value (square root of the intensity at the pupil plane) to obtain a new complex amplitude distribution. The new complex amplitude distribution is subjected to an inverse Fourier transformation to obtain the complex amplitude distribution on the focus plane. Again, a phase portion is left as it is, and the intensity is substituted with an actual measured value at the focus plane. By repeating the calculation described above to cause convergence, the complex amplitude distributions at the focus plane and the pupil plane are calculated. From the phase distribution of the complex amplitude distribution at the pupil plane, the wavefront aberration of the lens can be calculated.
However, in the case where the measurement of the intensity distribution at the pupil plane is difficult such as in the photolithography, the wavefront aberration of the optical system is calculated from the optical intensity distributions of the focus plane and a defocus plane. In Patent Document 2, the optical intensity distributions on a plurality of planes orthogonal to an optical axis and in the vicinity of the focus plane are respectively measured, the optical image complex amplitude near the focus plane or near the pupil plane is obtained by the phase restoration method, and then the wavefront aberration of the projection lens is obtained. Patent Document 3 focuses on the movement time of an optical intensity distribution measurement device when measuring the optical intensity distributions of the focus plane and the defocus plane. The optical intensity distribution of the pupil plane calculated from the optical intensity distributions of the focus plane and the defocus plane measured in advance is stored, the optical intensity distribution of a plane in the vicinity of the focus plane and orthogonal to the optical axis is measured at the time of the actual measurement, the complex amplitude distribution at the pupil plane is calculated using the phase restoration method from the optical intensity distribution in the vicinity of the focus plane and the stored optical intensity distribution of the pupil plane, and the wavefront aberration of a projection optical system is calculated from the complex amplitude distribution to ensure a real-time measurement.
Patent Document 1: Japanese Unexamined Patent Publication No. 08-271697
Patent Document 2: Japanese Patent No. 3634550
Patent Document 3: Japanese Patent No. 3774588
Non-Patent Document 1: Kazuto Yamauchi, Kazuya Yamamura, Hidekazu Mimura, Yasuhisa Sano, Akihisa Kubota, Yasuhiro Sekito, Kazumasa Ueno, Alexei Souvorov, Kenji Tamasaku, Makina Yabashi, Tetsuya Ishikawa, and Yuzo Mori: Development of the Shape Measurement System with Interferometers for Ultraprecise X-ray Mirror, Journal of the Japan Society of Precision Engineering, 69, (2003), 856